Answer:
D 20 *1.10 * 1.05
Step-by-step explanation:
We have 19.8 tons of wheat. That is close to 20 tons
We increase by 9.8 percent. 9.8% is close to 10%
When we increase, that is 100% of what we had plus the increase, so we multiply by 100 +10% or 110%. In decimal form that is 1.1
20 *1.10
Then the next year we increase by 5.1%. That is close to 5%
We have 100% plus the 5% or 105%, which in decimal form is 1.05
We multiply what we had (20 *1.10) by 1.05
20 *1.10 * 1.05
This is the total amount we have
Answer:
The bottom graph is the graph of that equation
Answer: The probability in (b) has higher probability than the probability in (a).
Explanation:
Since we're computing for the probability of the sample mean, we consider the z-score and the standard deviation of the sampling distribution. Recall that the standard deviation of the sampling distribution approximately the quotient of the population standard deviation and the square root of the sample size.
So, if the sample size higher, the standard deviation of the sampling distribution is lower. Since the sample size in (b) is higher, the standard deviation of the sampling distribution in (b) is lower.
Moreover, since the mean of the sampling distribution is the same as the population mean, the lower the standard deviation, the wider the range of z-scores. Because the standard deviation in (b) is lower, it has a wider range of z-scores.
Note that in a normal distribution, if the probability has wider range of z-scores, it has a higher probability. Therefore, the probability in (b) has higher probability than the probability in (a) because it has wider range of z-scores than the probability in (a).
Answer:
- The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is <u>translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis</u>.
Explanation:
By inspection (watching the figure), you can tell that to transform the triangle XY onto triangle X"Y"Z", you must slide the former 5 units to the left, 1 unit down, and, finally, reflect it across the x-axys.
You can check that analitically
Departing from the triangle: XYZ
- <u>Translation 5 units to the left</u>: (x,y) → (x - 5, y)
- Vertex X: (-6,2) → (-6 - 5, 2) = (-11,2)
- Vertex Y: (-4, 7) → (-4 - 5, 7) = (-9,7)
- Vertex Z: (-2, 2) → (-2 -5, 2) = (-7, 2)
- <u>Translation 1 unit down</u>: (x,y) → (x, y-1)
- (-11,2) → (-11, 2 - 1) = (-11, 1)
- (-9,7) → (-9, 7 - 1) = (-9, 6)
- (-7, 2) → (-7, 2 - 1) = (-7, 1)
- <u>Reflextion accross the x-axis</u>: (x,y) → (x, -y)
- (-11, 1) → (-11, -1), which are the coordinates of vertex X"
- (-9, 6) → (-9, -6), which are the coordinates of vertex Y""
- (-7, 1) → (-7, -1), which are the coordinates of vertex Z"
Thus, in conclusion, it is proved that the sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.
